Doctor of Philosophy
Three essays in financial asset pricing are given; one concerning the partial differential equation (PDE) pricing and hedging of a class of continuous/generalized power mean Asian options, via their (optimal) Lie point symmetry groups, leading to practical pricing formulas. The second presents high-frequency predictions of S&P 500 returns via several machine learning models, statistically significantly demonstrating short-horizon market predictability and economically significantly profitable (beyond transaction costs) trading strategies. The third compares profitability between these [(mean) ensemble] strategies and Asian option Δ-hedging, using results of the first. Interpreting bounds on arithmetic Asian option prices as ask and bid values, hedging profitability depends largely on securing prices closer to the bid, and settling midway between the bid and ask, significant profits are consistently accumulated during the years 2004-2016. Ensemble predictive trading the S&P 500 yields comparatively very small returns, despite trading much more frequently. The pricing and hedging of (arithmetic) Asian options are difficult and have spurred several solution approaches, differing in theoretical insight and practicality. Multiple families of exact solutions to relaxed power mean Asian option pricing boundary-value problems are explicitly established, which approximately satisfy the full pricing problem, and in one case, converge to exact solutions under certain parametric restrictions. Corresponding hedging parameters/ Greeks are derived. This family consists of (optimal) invariant solutions, constructed for the corresponding pricing PDEs. Numerical experiments explore this family behaviorally, achieving reliably accurate pricing. The second chapter studies intraday market return predictability. Regularized linear and nonlinear tree-based models enjoy significant predictability. Ensemble models perform best across time and their return predictability realizes economically significant profits with Sharpe ratios after transaction costs of 0.98. These results strongly evidence that intraday market returns are predictable during short time horizons, beyond that explainable by transaction costs. The lagged constituent returns are shown to hold significant predictive information not contained in lagged market returns or price trend and liquidity characteristics. Consistent with the hypothesis that predictability is driven by slow-moving trader capital, predictability decreased post-decimalization, and market returns are more predictable midday, on days with high volatility or illiquidity, and during financial crises.
Summary for Lay Audience
The pricing of two financial goods (options and stocks) is studied in three essays: One examines both the pricing and portfolio/risk management of a large family of options which encapsulates others previously proposed and studied. The second predicts five-minute samples of S&P 500 returns via several machine learning models: Statistically and economically significant results follow through trading strategies that are profitable beyond transaction costs. The third compares profitability between these strategies and others which follow from the portfolio/risk management results for options. In a framework with a trader deciding to engage in such portfolio management/optimization from day to day, given ask and bid option prices, profitability depends largely on securing prices closer to the bid, and settling midway between the bid and ask, significant profits are consistently accumulated during the years 2004-2016. Trading the S&P 500 using the machine learning results yields comparatively very small returns, despite trading much more frequently.
Option pricing and portfolio/risk management are difficult and have spurred several solution approaches, differing in theoretical insight and practicality. Multiple families of option pricing formulas are explicitly established, which approximately satisfy the full pricing problem, and in one case, are exact under certain restrictions. Corresponding risk management parameters are derived, and numerical experiments explore these families behaviorally, achieving practical, reliably accurate pricing.
The second chapter predicts five-minute market returns using models of varying sophistication and complexity. Models that average results of others perform best and yield economically significant and reliable profits after transaction costs which nearly equal their standard deviation. These results strongly evidence that five-minute market returns are predictable, beyond what can be explained by (trading behaviour due to) transaction costs. Returns of the (500) market constituents are shown to hold significant predictive information not contained in those of the S&P 500 alone; or statistics that characterize market solvency. Consistent with the hypothesis that slow-moving trader capital drives predictability, the latter decreased in the early millennium when various technological and regulatory factors increased market solvency. Similarly, market returns are more predictable on highly volatile or insolvent days/times and particularly during financial crises.
Huddleston, Dillon Ross, "Essays in financial asset pricing" (2021). Electronic Thesis and Dissertation Repository. 8292.
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